Network equilibrium with mixed behavior

Abstract

The classical Wardropian principle hypothesize that users minimize either individual travel cost or overall system cost. In reality, users do not always behave in such a manner; instead, they are both competing and cooperating, typically when there exists oligopoly Cournot-Nash firms. In this paper, we formulate a mixed network equilibrium model as variational inequalities (VI) that simultaneously describe the routing behaviors of user equilibrium (UE), system optimum (SO) and Cournot-Nash (CN) players. Each player is presumed to make a routing decision given the knowledge of the routing strategies of the other players. After examining the existence and uniqueness of solutions, the diagonalization approach is applied to find a mixed equilibrium solution.